Quasiperiodic modulation can prevent isolated quantum systems from equilibrating by localizing their degrees of freedom. Such localization has been well-known since the work of Aubry and André and, in modern quantum optical systems, quasiperiodic `disorder' has become a standard tool for inducing Anderson localization.
In this talk, I will describe how the interplay of symmetry breaking and localization in the presence of quasiperiodic modulation leads to a surprisingly rich range of phenomena in transverse field Ising chains. I will begin with the phase diagram at zero temperature, which exhibits paramagnetic and ferromagnetic phases with localized or extended low-energy excitations. We will discover a robust new quantum Ising transition whose properties are intermediate between those of the clean and random Ising transitions. We will then turn the dynamical phases at 'infinite temperature', where we will find a 'quasiperiodic Ising glass' phase with dynamical order protected by localization. We will discuss melting transitions out of this glass phase and new dualities in the quasiperiodic Ising model.
Faculty Host: Yuan-ming Lu
